However, in real-world problems, the future evolution of the arrival process and/or the service process is
often influenced by the past events.
This is essentially observed, during periods of suffering, for instance earthquakes, crime and riots
and social media trend (Daw and Pender
[1]},
and
Rizoiu et al.
[2]}) and in the financial market, incorporating some kind of contagion effect
(Aït-Sahalia et al.
[3]}).
Recently, the same phenomenon is observed to describe the temporal growth and migration of COVID-19
(see Chiang et al.
[4]}, Escobar [5]}, Garetto et al.
[6]}).
The work by Eick et al.
[7]}, and recent works by Daw and Pender
[1]} and Koops et al. [9]},
motivated us to consider the service process as a state-dependent Hawkes (sdHawkes) process.
